Function opendp::accuracy::discrete_laplacian_scale_to_accuracy

pub fn discrete_laplacian_scale_to_accuracy<T: Float + Zero + One + Debug>(
    scale: T,
    alpha: T
) -> Fallible<T>

Convert a discrete Laplacian scale into an accuracy estimate (tolerance) at a statistical significance level alpha.

$\alpha = P[Y \ge accuracy]$, where $Y = |X - z|$, and $X \sim \mathcal{L}_{Z}(0, scale)$. That is, $X$ is a discrete Laplace random variable and $Y$ is the distribution of the errors.

This function returns a float accuracy. You can take the floor without affecting the coverage probability.

Arguments

• scale - Discrete Laplacian noise scale.
• alpha - Statistical significance, level-alpha, or (1. - alpha)100% confidence. Must be within (0, 1].

Generics

• T - Data type of scale and alpha

Proof Definition

(Proof Document)